Mathematical approach to modelling sigmoidal power curves for Wind Energy Conversion Systems

The output power of a wind turbine is usually found to follow a sigmoid curve as a function of wind speed. As a result, identifying the appropriate sigmoid curve to fit the wind turbine power curve is crucial for maximizing the turbine's performance. In this paper, we analyse the effectiveness of several renowned sigmoid functions to correctly model the power curve of a wind turbine with minimum convergence error and reduced complexity. The Logistic and Hill functions are among the candidates. We show that all of the aforementioned sigmoid functions are best suited for modelling WEC power curves if the sigmoid functions' parameters are appropriately determined and adjusted to account for the delay in the power response and to perform as a cubic function in the wind speed locally. When it comes to interpreting the physical meaning of the underlying parameters, they each have their own advantages and drawbacks. Experimental data from a wind farm in Mauritius is used to validate the model.